Multiple Imputation Standard Errors - Survey-Kit

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# Multiple Imputation Standard Errors

## mi_ses_from_function

    mi_ses_from_function(
        delegate: Callable,
        join_on: list,
        path_srmi: str = "",
        df_implicates: list[IntoFrameT]
        | DataFrameList
        | None = None,
        index: list | None = None,
        df_noimputes: IntoFrameT | None = None,
        arguments: dict | None = None,
        df_argument_name: str = "df",
        implicate_name: str = "___implicate___",
        parallel: bool = False,
        parallel_inputs: CallInputs | None = None,
        rounding: Rounding | None = None,
        round_output: bool = True,
    ) -> MultipleImputation

Calculate multiple imputation standard errors by applying a function to each implicate.

This is the main function for computing MI estimates. It applies a specified function (delegate) to each imputed dataset, then combines the results using Rubin's rules to produce final estimates with proper MI standard errors.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`delegate` | `callable` | Function to apply to each imputed dataset. Should return estimates, standard errors, and optionally replicate estimates. Common choices: - StatCalculator class constructor - Custom analysis function | required
`path_srmi` | `str` | The path to a saved SRMI serialized object The default is "". Must pass either path_srmi or df_implicates | `''`
`df_implicates` | `list[IntoFrameT] | DataFrameList` | List of imputed datasets to analyze. The default is None Must pass either path_srmi or df_implicates | `None`
`join_on` | `list` | Column names that identify unique estimates across implicates. Used for combining results. | required
`index` | `list | None` | Index columns for merging df_noimputes with implicates. If None, assumes row-wise concatenation (dangerous...). Default is None. | `None`
`df_noimputes` | `IntoFrameT | None` | Non-imputed data (e.g., weights, design variables) to merge with each implicate. Default is None. | `None`
`arguments` | `dict | None` | Additional arguments passed to the delegate function. Default is None. | `None`
`df_argument_name` | `str` | Name of the dataframe argument in the delegate function. Default is "df". | `'df'`
`parallel` | `bool` | Run analysis on implicates in parallel. Default is False. | `False`
`parallel_inputs` | `CallInputs | None` | Configuration for parallel execution. Default is None. | `None`
`rounding` | `Rounding | None` | Rounding configuration for results. Default is None. | `None`
`round_output` | `bool` | Apply rounding to final output. Default is True. | `True`

Returns:

Type | Description
--- | ---
`MultipleImputation` | MultipleImputation object containing combined estimates, MI standard errors, degrees of freedom, and other MI diagnostics.

Examples:

Basic usage with StatCalculator:

    >>> from NEWS.CodeUtilities.Python.Statistics.StatCalculator import StatCalculator
    >>> from NEWS.CodeUtilities.Python.SummaryStats import Statistics, Replicates
    >>> from NEWS.CodeUtilities.Python.SRMI.SRMI import SRMI
    >>>
    >>> # Load SRMI data
    >>> srmi = SRMI.load(path_model="/projects/data/NEWS/Test/py_srmi_test.srmi/",
    ...                  LazyLoad=False)
    >>>
    >>>
    >>> # Define what to calculate
    >>> stats = Statistics(stats=["mean", "median"], columns=["income", "age"])
    >>> replicates = Replicates(weight_stub="replicate_", n_replicates=80)
    >>>
    >>> # Arguments for StatCalculator
    >>> arguments = {
    ...     "statistics": stats,
    ...     "replicates": replicates,
    ...     "weight": "survey_weight",
    ...     "display": False
    ... }
    >>>
    >>> # Calculate MI estimates
    >>> mi_results = mi_ses_from_function(
    ...     delegate=StatCalculator,
    ...     df_implicates=srmi.df_implicates,
    ...     df_noimputes=weight_data,
    ...     arguments=arguments,
    ...     join_on=["Variable"]
    ... )
    >>>
    >>> # View results
    >>> mi_results.print(round_output=True)
    >>> print("Degrees of freedom:", mi_results.df_df)
    >>> print("Missing information rate:", mi_results.df_rate_of_missing_information)

With a custom analysis function:

    >>> def custom_analysis(df, weight="", var="income"):
    ...     '''Custom function returning estimates'''
    ...     import polars as pl
    ...
    ...     if weight:
    ...         mean_est = (df[var] * df[weight]).sum() / df[weight].sum()
    ...     else:
    ...         mean_est = df[var].mean()
    ...
    ...     return pl.DataFrame({
    ...         "Variable": [var],
    ...         "estimate": [mean_est]
    ...     })
    >>>
    >>> mi_custom = mi_ses_from_function(
    ...     delegate=custom_analysis,
    ...     df_implicates=srmi.df_implicates,
    ...     arguments={"weight": "survey_weight", "var": "income"},
    ...     join_on=["Variable"]
    ... )

Parallel processing for faster computation:

    >>> from NEWS.CodeUtilities.Python.Function.Utilities import CallInputs, CallTypes
    >>>
    >>> parallel_config = CallInputs(CallType=CallTypes.shell)
    >>> mi_results = mi_ses_from_function(
    ...     delegate=StatCalculator,
    ...     df_implicates=srmi.df_implicates,
    ...     arguments=arguments,
    ...     join_on=["Variable"],
    ...     parallel=True,
    ...     parallel_inputs=parallel_config
    ... )

Notes

The function implements the standard MI workflow: 1. Apply delegate function to each imputed dataset 2. Collect estimates and SEs from each implicate 3. Combine using Rubin's rules for MI inference 4. Calculate degrees of freedom and missing information rates

For delegate functions that return tuples/lists, expects: - Item 0: estimates dataframe - Item 1: standard errors dataframe - Item 2: replicate estimates (optional) - Item 3: bootstrap flag (optional)

See Also

`StatCalculator` : Main class for statistical calculations `MultipleImputation` : Class for MI results

Source code in `src\survey_kit\statistics\multiple_imputation.py`

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    def mi_ses_from_function(
        delegate: Callable,
        join_on: list,
        path_srmi: str = "",
        df_implicates: list[IntoFrameT] | DataFrameList | None = None,
        index: list | None = None,
        df_noimputes: IntoFrameT | None = None,
        arguments: dict | None = None,
        df_argument_name: str = "df",
        implicate_name: str = "___implicate___",
        parallel: bool = False,
        parallel_inputs: CallInputs | None = None,
        rounding: Rounding | None = None,
        round_output: bool = True,
    ) -> MultipleImputation:
        """
        Calculate multiple imputation standard errors by applying a function to each implicate.

        This is the main function for computing MI estimates. It applies a specified function
        (delegate) to each imputed dataset, then combines the results using Rubin's rules
        to produce final estimates with proper MI standard errors.

        Parameters
        ----------
        delegate : callable
            Function to apply to each imputed dataset. Should return estimates,
            standard errors, and optionally replicate estimates. Common choices:
            - StatCalculator class constructor
            - Custom analysis function
        path_srmi : str, optional
            The path to a saved SRMI serialized object
            The default is "".
            Must pass either path_srmi or df_implicates
        df_implicates : list[IntoFrameT] | DataFrameList, optional
            List of imputed datasets to analyze.
            The default is None
            Must pass either path_srmi or df_implicates
        join_on : list
            Column names that identify unique estimates across implicates.
            Used for combining results.
        index : list|None, optional
            Index columns for merging df_noimputes with implicates.
            If None, assumes row-wise concatenation (dangerous...). Default is None.
        df_noimputes : IntoFrameT | None, optional
            Non-imputed data (e.g., weights, design variables) to merge with
            each implicate. Default is None.
        arguments : dict|None, optional
            Additional arguments passed to the delegate function. Default is None.
        df_argument_name : str, optional
            Name of the dataframe argument in the delegate function. Default is "df".
        parallel : bool, optional
            Run analysis on implicates in parallel. Default is False.
        parallel_inputs : CallInputs | None, optional
            Configuration for parallel execution. Default is None.
        rounding : Rounding | None, optional
            Rounding configuration for results. Default is None.
        round_output : bool, optional
            Apply rounding to final output. Default is True.

        Returns
        -------
        MultipleImputation
            MultipleImputation object containing combined estimates, MI standard errors,
            degrees of freedom, and other MI diagnostics.

        Examples
        --------
        Basic usage with StatCalculator:

        >>> from NEWS.CodeUtilities.Python.Statistics.StatCalculator import StatCalculator
        >>> from NEWS.CodeUtilities.Python.SummaryStats import Statistics, Replicates
        >>> from NEWS.CodeUtilities.Python.SRMI.SRMI import SRMI
        >>>
        >>> # Load SRMI data
        >>> srmi = SRMI.load(path_model="/projects/data/NEWS/Test/py_srmi_test.srmi/",
        ...                  LazyLoad=False)
        >>>
        >>>
        >>> # Define what to calculate
        >>> stats = Statistics(stats=["mean", "median"], columns=["income", "age"])
        >>> replicates = Replicates(weight_stub="replicate_", n_replicates=80)
        >>>
        >>> # Arguments for StatCalculator
        >>> arguments = {
        ...     "statistics": stats,
        ...     "replicates": replicates,
        ...     "weight": "survey_weight",
        ...     "display": False
        ... }
        >>>
        >>> # Calculate MI estimates
        >>> mi_results = mi_ses_from_function(
        ...     delegate=StatCalculator,
        ...     df_implicates=srmi.df_implicates,
        ...     df_noimputes=weight_data,
        ...     arguments=arguments,
        ...     join_on=["Variable"]
        ... )
        >>>
        >>> # View results
        >>> mi_results.print(round_output=True)
        >>> print("Degrees of freedom:", mi_results.df_df)
        >>> print("Missing information rate:", mi_results.df_rate_of_missing_information)

        With a custom analysis function:

        >>> def custom_analysis(df, weight="", var="income"):
        ...     '''Custom function returning estimates'''
        ...     import polars as pl
        ...
        ...     if weight:
        ...         mean_est = (df[var] * df[weight]).sum() / df[weight].sum()
        ...     else:
        ...         mean_est = df[var].mean()
        ...
        ...     return pl.DataFrame({
        ...         "Variable": [var],
        ...         "estimate": [mean_est]
        ...     })
        >>>
        >>> mi_custom = mi_ses_from_function(
        ...     delegate=custom_analysis,
        ...     df_implicates=srmi.df_implicates,
        ...     arguments={"weight": "survey_weight", "var": "income"},
        ...     join_on=["Variable"]
        ... )

        Parallel processing for faster computation:

        >>> from NEWS.CodeUtilities.Python.Function.Utilities import CallInputs, CallTypes
        >>>
        >>> parallel_config = CallInputs(CallType=CallTypes.shell)
        >>> mi_results = mi_ses_from_function(
        ...     delegate=StatCalculator,
        ...     df_implicates=srmi.df_implicates,
        ...     arguments=arguments,
        ...     join_on=["Variable"],
        ...     parallel=True,
        ...     parallel_inputs=parallel_config
        ... )

        Notes
        -----
        The function implements the standard MI workflow:
        1. Apply delegate function to each imputed dataset
        2. Collect estimates and SEs from each implicate
        3. Combine using Rubin's rules for MI inference
        4. Calculate degrees of freedom and missing information rates

        For delegate functions that return tuples/lists, expects:
        - Item 0: estimates dataframe
        - Item 1: standard errors dataframe
        - Item 2: replicate estimates (optional)
        - Item 3: bootstrap flag (optional)

        See Also
        --------
        [`StatCalculator`][survey_kit.statistics.calculator.StatCalculator] : Main class for statistical calculations
        [`MultipleImputation`][survey_kit.statistics.multiple_imputation.MultipleImputation] : Class for MI results
        """

        #   Don't edit the arguments dictionary
        arguments = copy(arguments)
        if parallel:
            if path_srmi != "":
                n_implicates = SRMI.load(path_srmi).n_implicates
            else:
                n_implicates = len(df_implicates)
            if parallel_inputs is None:
                logger.info("Defaulting to shell for parallel estimation")
                parallel_inputs = CallInputs(
                    call_type=CallTypes.shell, n_cpu=int(config.cpus / n_implicates)
                )

            del n_implicates
            arguments = locals().copy()

            implicate_stats = _mi_ses_from_function_parallel(**arguments)

        else:
            arguments = locals().copy()

            del arguments["parallel"]
            del arguments["parallel_inputs"]
            implicate_stats = _mi_ses_from_function_sequential(**arguments)

        if len(implicate_stats):
            mi_stats = MultipleImputation(
                implicate_stats=implicate_stats, join_on=join_on, rounding=rounding
            )
            mi_stats.calculate()

            return mi_stats

        else:
            return None

## MultipleImputation

Bases: `Serializable`

A class for managing multiple imputation standard errors. You should generally estimate the statistics with `mi_ses_from_function` and then use this class to do comparisons, print, or gather results from the dataframes in it.

MultipleImputation combines estimates from multiple imputed datasets to produce final estimates with proper standard errors that account for both within-imputation and between-imputation variance. It implements Rubin's rules for multiple imputation inference, including degrees of freedom calculations and missing information rates.

The class supports: - Combining estimates from multiple imputed datasets - Calculating proper MI standard errors using Rubin's rules - Computing degrees of freedom for t-tests with MI data - Calculating rates of missing information - Statistical comparisons between MI estimate sets - Confidence intervals and p-values adjusted for MI uncertainty - Integration with replicate weight variance estimation

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`implicate_stats` | `list[ReplicateStats] | None` | List of ReplicateStats objects, one for each imputed dataset. Each contains estimates and potentially replicate weight SEs. Default is None. | `None`
`join_on` | `list | None` | Column names that identify unique estimates across implicates. Used for combining estimates. Default is None (empty list). | `None`
`df_estimates` | `IntoFrameT | None` | Combined estimates dataframe (calculated automatically). Default is None. | `None`
`df_ses` | `IntoFrameT | None` | MI standard errors dataframe (calculated automatically). Default is None. | `None`
`df_df` | `IntoFrameT | None` | Degrees of freedom for each estimate (calculated automatically). Default is None. | `None`
`df_t` | `IntoFrameT | None` | T-statistics dataframe (calculated automatically). Default is None. | `None`
`df_p` | `IntoFrameT | None` | P-values dataframe (calculated automatically). Default is None. | `None`
`df_rate_of_missing_information` | `IntoFrameT | None` | Rate of missing information for each estimate. Default is None. | `None`
`rounding` | `Rounding | None` | Rounding configuration for display and output. Default is None. | `None`

Attributes:

Name | Type | Description
--- | --- | ---
`n_implicates` | `int` | Number of imputed datasets used in the analysis.
`summarize_vars` | `list` | List of all estimate column names (excluding join variables).

Examples:

Creating MI estimates from a function applied to multiple implicates:

    >>> from survey_kit.statistics.multiple_imputation import mi_ses_from_function
    >>> from survey_kit.statistics.calculator import StatCalculator
    >>> from survey_kit.statistics.statistics import Statistics
    >>> from survey_kit.imputation.srmi import SRMI
    >>>
    >>> # Define statistics to calculate
    >>> stats = Statistics(stats=["mean"], columns=["var_*"])
    >>> replicates = Replicates(weight_stub="weight_", n_replicates=20)
    >>>
    >>> # Arguments for the function to run on each implicate
    >>> arguments = {
    ...     "statistics": stats,
    ...     "replicates": replicates,
    ...     "round_output": False,
    ...     "display": False
    ... }
    >>> # Load SRMI data
    >>> srmi = SRMI.load(path_model="/projects/data/NEWS/Test/py_srmi_test.srmi/",
    ...                  LazyLoad=False)
    >>>
    >>> # Calculate MI estimates
    >>> mi_results = mi_ses_from_function(
    ...     delegate=StatCalculator,
    ...     df_implicates=srmi.df_implicates,
    ...     df_noimputes=weights_data,
    ...     arguments=arguments,
    ...     join_on=["Variable"]
    ... )
    >>> mi_results.print(round_output=True)

Comparing two sets of MI estimates:

    >>> mi_means = mi_ses_from_function(...)  # Calculate means
    >>> mi_medians = mi_ses_from_function(...)  # Calculate medians
    >>>
    >>> comparison = mi_means.compare(
    ...     mi_medians,
    ...     compare_list_columns=[("mean", "median")]
    ... )
    >>> comparison["difference"].print()
    >>> comparison["ratio"].print()

Examining MI-specific diagnostics:

    >>> print("Degrees of freedom:")
    >>> print(mi_results.df_df)
    >>> print("Rate of missing information:")
    >>> print(mi_results.df_rate_of_missing_information)

Notes

The class implements Rubin's (1987) rules for multiple imputation: - Combined estimate is the average across implicates - Total variance = within-imputation variance + between-imputation variance - Degrees of freedom account for finite number of implicates - Missing information rate quantifies uncertainty due to imputation

Source code in `src\survey_kit\statistics\multiple_imputation.py`

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    class MultipleImputation(Serializable):
        """
        A class for managing multiple imputation standard errors.  You should generally estimate
        the statistics with [`mi_ses_from_function`][survey_kit.statistics.multiple_imputation.mi_ses_from_function] and then use this class to
        do comparisons, print, or gather results from the dataframes in it.

        MultipleImputation combines estimates from multiple imputed datasets to produce
        final estimates with proper standard errors that account for both within-imputation
        and between-imputation variance. It implements Rubin's rules for multiple imputation
        inference, including degrees of freedom calculations and missing information rates.

        The class supports:
        - Combining estimates from multiple imputed datasets
        - Calculating proper MI standard errors using Rubin's rules
        - Computing degrees of freedom for t-tests with MI data
        - Calculating rates of missing information
        - Statistical comparisons between MI estimate sets
        - Confidence intervals and p-values adjusted for MI uncertainty
        - Integration with replicate weight variance estimation

        Parameters
        ----------
        implicate_stats : list[ReplicateStats] | None, optional
            List of ReplicateStats objects, one for each imputed dataset.
            Each contains estimates and potentially replicate weight SEs. Default is None.
        join_on : list | None, optional
            Column names that identify unique estimates across implicates.
            Used for combining estimates. Default is None (empty list).
        df_estimates : IntoFrameT | None, optional
            Combined estimates dataframe (calculated automatically). Default is None.
        df_ses : IntoFrameT | None, optional
            MI standard errors dataframe (calculated automatically). Default is None.
        df_df : IntoFrameT | None, optional
            Degrees of freedom for each estimate (calculated automatically). Default is None.
        df_t : IntoFrameT | None, optional
            T-statistics dataframe (calculated automatically). Default is None.
        df_p : IntoFrameT | None, optional
            P-values dataframe (calculated automatically). Default is None.
        df_rate_of_missing_information : IntoFrameT | None, optional
            Rate of missing information for each estimate. Default is None.
        rounding : Rounding | None, optional
            Rounding configuration for display and output. Default is None.

        Attributes
        ----------
        n_implicates : int
            Number of imputed datasets used in the analysis.
        summarize_vars : list
            List of all estimate column names (excluding join variables).

        Examples
        --------
        Creating MI estimates from a function applied to multiple implicates:

        >>> from survey_kit.statistics.multiple_imputation import mi_ses_from_function
        >>> from survey_kit.statistics.calculator import StatCalculator
        >>> from survey_kit.statistics.statistics import Statistics
        >>> from survey_kit.imputation.srmi import SRMI
        >>>
        >>> # Define statistics to calculate
        >>> stats = Statistics(stats=["mean"], columns=["var_*"])
        >>> replicates = Replicates(weight_stub="weight_", n_replicates=20)
        >>>
        >>> # Arguments for the function to run on each implicate
        >>> arguments = {
        ...     "statistics": stats,
        ...     "replicates": replicates,
        ...     "round_output": False,
        ...     "display": False
        ... }
        >>> # Load SRMI data
        >>> srmi = SRMI.load(path_model="/projects/data/NEWS/Test/py_srmi_test.srmi/",
        ...                  LazyLoad=False)
        >>>
        >>> # Calculate MI estimates
        >>> mi_results = mi_ses_from_function(
        ...     delegate=StatCalculator,
        ...     df_implicates=srmi.df_implicates,
        ...     df_noimputes=weights_data,
        ...     arguments=arguments,
        ...     join_on=["Variable"]
        ... )
        >>> mi_results.print(round_output=True)

        Comparing two sets of MI estimates:

        >>> mi_means = mi_ses_from_function(...)  # Calculate means
        >>> mi_medians = mi_ses_from_function(...)  # Calculate medians
        >>>
        >>> comparison = mi_means.compare(
        ...     mi_medians,
        ...     compare_list_columns=[("mean", "median")]
        ... )
        >>> comparison["difference"].print()
        >>> comparison["ratio"].print()

        Examining MI-specific diagnostics:

        >>> print("Degrees of freedom:")
        >>> print(mi_results.df_df)
        >>> print("Rate of missing information:")
        >>> print(mi_results.df_rate_of_missing_information)

        Notes
        -----
        The class implements Rubin's (1987) rules for multiple imputation:
        - Combined estimate is the average across implicates
        - Total variance = within-imputation variance + between-imputation variance
        - Degrees of freedom account for finite number of implicates
        - Missing information rate quantifies uncertainty due to imputation

        """

        _save_suffix = "mi"

        def __init__(
            self,
            implicate_stats: list[ReplicateStats] | None = None,
            join_on: list | None = None,
            df_estimates: IntoFrameT | None = None,
            df_ses: IntoFrameT | None = None,
            df_df: IntoFrameT | None = None,
            df_t: IntoFrameT | None = None,
            df_p: IntoFrameT | None = None,
            df_rate_of_missing_information: IntoFrameT | None = None,
            rounding: Rounding | None = None,
        ):
            self.implicate_stats = implicate_stats

            if join_on is None:
                join_on = []
            self.join_on = join_on
            self.df_estimates = df_estimates
            self.df_ses = df_ses
            self.df_df = df_df
            self.df_t = df_t
            self.df_p = df_p
            self.df_rate_of_missing_information = df_rate_of_missing_information
            self.rounding = rounding

        def copy(self) -> MultipleImputation:
            return MultipleImputation(
                implicate_stats=[impi.copy() for impi in self.implicate_stats],
                join_on=copy(self.join_on),
                df_estimates=self.df_estimates,
                df_ses=self.df_ses,
                df_df=self.df_df,
                df_t=self.df_t,
                df_p=self.df_p,
                df_rate_of_missing_information=self.df_rate_of_missing_information,
                rounding=copy(self.rounding),
            )

        def calculate(self, implicate_name="___implicate___"):
            """
            Calculate multiple imputation estimates using Rubin's rules.

            Combines estimates from individual implicates to produce final MI estimates,
            standard errors, degrees of freedom, t-statistics, p-values, and rates of
            missing information. Implements the standard MI combining formulas.

            Parameters
            ----------
            implicate_name : str, optional
                Column name identifier for imputation number. Default is "___implicate___".

            Notes
            -----
            Implements Rubin's combining rules:
            - Q̄ = (1/m) Σ Q̂ᵢ  (combined estimate)
            - U = (1/m) Σ Uᵢ    (within-imputation variance)
            - B = (1/(m-1)) Σ (Q̂ᵢ - Q̄)²  (between-imputation variance)
            - T = U + (1 + 1/m)B  (total variance)
            - ν = (m-1)[1 + mU/((m+1)B)]²  (degrees of freedom)

            where m is the number of implicates.
            """

            df_estimates_stacked = []
            df_ses_stacked = []

            col_sort = "___mi_sort___"
            for indexi, imp_statsi in enumerate(self.implicate_stats):
                if indexi == 0:
                    df_sort = (
                        nw.from_native(imp_statsi.df_estimates)
                        .select(self.join_on)
                        .lazy()
                        .collect()
                        .with_row_index(col_sort)
                        .lazy()
                        .to_native()
                    )
                df_estimates_stacked.append(imp_statsi.df_estimates)
                df_ses_stacked.append(imp_statsi.df_ses)

            df_estimates_stacked = (
                nw.from_native(
                    fill_missing(
                        concat_wrapper(df_estimates_stacked, how="diagonal"),
                        value=float("nan"),
                    )
                )
                .lazy()
                .collect()
                .to_native()
            )
            df_ses_stacked = (
                nw.from_native(concat_wrapper(df_ses_stacked, how="diagonal"))
                .with_columns(cs.boolean().cast(nw.Int8))
                .lazy()
                .collect()
                .to_native()
            )

            cols_non_stats = self.join_on + [implicate_name, col_sort]
            cols_stats = safe_columns(df_estimates_stacked)
            cols_stats = _columns_original_order(
                columns_unordered=list(set(cols_stats).difference(cols_non_stats)),
                columns_ordered=cols_stats,
            )

            #   Notation from Joe Schaffer MI FAQ page (downloaded from the Wayback Machine)
            #       NEWS/Documentation/Background/MultipleImputation/MI_FAQ.htm
            df_estimates = (
                nw.from_native(df_estimates_stacked)
                .group_by(self.join_on)
                .agg(nw.all().mean())
                .sort(self.join_on)
            )

            c_stats = nw.col(cols_stats)
            with_between = []
            for coli in cols_stats:
                c_col = nw.col(coli)
                c_bar = nw.col(f"{coli}_bar")
                with_between.append(
                    (1 / (self.n_implicates - 1) * (c_col - c_bar) ** 2).alias(coli)
                )

            df_B = (
                nw.from_native(
                    join_list(
                        [
                            df_estimates_stacked,
                            (
                                nw.from_native(df_estimates)
                                .rename({coli: f"{coli}_bar" for coli in cols_stats})
                                .to_native()
                            ),
                        ],
                        on=self.join_on,
                        how="left",
                    )
                )
                .with_columns(with_between)
                .group_by(self.join_on)
                .agg(c_stats.sum())
                .to_native()
            )

            df_U = (
                nw.from_native(df_ses_stacked)
                .with_columns(c_stats**2)
                .group_by(self.join_on)
                .agg(nw.all().mean())
                .to_native()
            )

            df_variance = (
                nw.from_native(
                    concat_wrapper(
                        [
                            nw.from_native(df_B)
                            .with_columns(c_stats * (1 + 1 / self.n_implicates))
                            .to_native(),
                            df_U,
                        ],
                        how="diagonal",
                    )
                )
                .group_by(self.join_on)
                .agg(nw.all().sum())
                .to_native()
            )

            self.df_ses = nw.from_native(df_variance).with_columns(c_stats**0.5).to_native()

            self.df_estimates = (
                nw.from_native(df_estimates_stacked)
                .group_by(self.join_on)
                .agg(nw.all().mean())
                .sort(self.join_on)
                .to_native()
            )

            df_B_U = join_list(
                [
                    (
                        nw.from_native(df_B)
                        .rename({coli: f"{coli}_B" for coli in cols_stats})
                        .to_native()
                    ),
                    (
                        nw.from_native(df_U)
                        .rename({coli: f"{coli}_U" for coli in cols_stats})
                        .to_native()
                    ),
                ],
                on=self.join_on,
                how="left",
            )

            m = self.n_implicates
            with_df = []
            for coli in cols_stats:
                c_U = nw.col(f"{coli}_U")
                c_B = nw.col(f"{coli}_B")

                with_df.append(
                    ((m - 1) * (1 + (m * c_U) / ((m + 1) * c_B)) ** 2).alias(coli)
                )

            self.df_df = nw.from_native(df_B_U).select(self.join_on + with_df).to_native()

            with_r = []
            with_gamma = []
            for coli in cols_stats:
                c_U = nw.col(f"{coli}_U")
                c_B = nw.col(f"{coli}_B")
                c_r = nw.col(f"{coli}_r")
                c_df = nw.col(f"{coli}_df")
                with_r.append(((1 + 1 / m) * c_B / c_U).alias(f"{coli}_r"))

                with_gamma.append(((c_r + (2 / (c_df + 3))) / (c_r + 1)).alias(coli))

            self.df_rate_of_missing_information = (
                nw.from_native(
                    join_list(
                        [
                            df_B_U,
                            (
                                nw.from_native(self.df_df)
                                .rename({coli: f"{coli}_df" for coli in cols_stats})
                                .to_native()
                            ),
                        ],
                        how="left",
                        on=self.join_on,
                    )
                )
                .with_columns(with_r)
                .select(self.join_on + with_gamma)
                .to_native()
            )

            with_t = []
            for coli in cols_stats:
                c_est = nw.col(coli)
                c_se = nw.col(f"{coli}_se")

                with_t.append((c_est / c_se).abs().alias(coli))

            self.df_t = (
                nw.from_native(
                    join_list(
                        [
                            self.df_estimates,
                            (
                                nw.from_native(self.df_ses)
                                .rename({coli: f"{coli}_se" for coli in cols_stats})
                                .to_native()
                            ),
                        ],
                        on=self.join_on,
                        how="left",
                    )
                )
                .select(self.join_on + with_t)
                .to_native()
            )

            df_p = join_list(
                [
                    (
                        nw.from_native(self.df_df)
                        .rename({coli: f"{coli}_df" for coli in cols_stats})
                        .to_native()
                    ),
                    (
                        nw.from_native(self.df_t)
                        .rename({coli: f"{coli}_t" for coli in cols_stats})
                        .to_native()
                    ),
                ],
                how="left",
                on=self.join_on,
            )

            def p_value(t, df):
                if t == float("inf") or t == float("nan"):
                    return 0
                if df == float("inf") or df == float("nan"):
                    df = 1_000_000

                return scipy.stats.t.sf(t, df) * 2

            def p_value_lambda(t, col_t, col_df):
                try:
                    return p_value(t[col_t], t[col_df])
                except:
                    return None

            nw_type = NarwhalsType(df_p)
            df_p = nw_type.to_polars().lazy().collect()
            for coli in cols_stats:
                index_t = df_p.columns.index(f"{coli}_t")
                index_df = df_p.columns.index(f"{coli}_df")

                df_p = df_p.with_columns(
                    df_p.map_rows(
                        lambda t: p_value_lambda(t, index_t, index_df),
                        return_dtype=pl.Float64,
                    )
                ).rename({"map": coli})

            self.df_p = nw_type.from_polars(df_p.select(self.join_on + cols_stats))

            def _sort_and_fill_null(df: IntoFrameT) -> IntoFrameT:
                nw_type = NarwhalsType(
                    join_list([df, df_sort], how="left", on=self.join_on)
                )
                return nw_type.from_polars(
                    nw_type.to_polars()
                    .sort([col_sort], maintain_order=True)
                    .drop(col_sort)
                    .fill_nan(None)
                )

            self.df_estimates = _sort_and_fill_null(self.df_estimates)
            self.df_ses = _sort_and_fill_null(self.df_ses)
            self.df_df = _sort_and_fill_null(self.df_df)
            self.df_t = _sort_and_fill_null(self.df_t)
            self.df_p = _sort_and_fill_null(df_p)
            self.df_rate_of_missing_information = _sort_and_fill_null(
                self.df_rate_of_missing_information
            )

        def compare(
            self,
            other: ReplicateStats | MultipleImputation | StatCalculator,
            difference: bool = True,
            ratio: bool = True,
            ratio_minus_1: bool = True,
            replicate_name: str = "___replicate___",
            compare_list_variables: list[ComparisonItem.Variable] | None = None,
            compare_list_columns: list[ComparisonItem.Column] | None = None,
        ) -> dict[str, MultipleImputation]:
            """
            Compare this set of MI estimates to another set of estimates.

            Parameters
            ----------
            other : MultipleImputation | ReplicateStats | StatCalculator
                The other object to compare against.
            difference : bool, optional
                Calculate and return differences. Default is True.
            ratio : bool, optional
                Calculate and return ratios. Default is True.
            ratio_minus_1 : bool, optional
                Subtract 1 from ratios (for percentage change interpretation).
                Default is True.
            replicate_name : str, optional
                Column name for replicate identifier. Default is "___replicate___".
            compare_list_variables : list[ComparisonItem.Variable] | None, optional
                List of variable info to compare.
            compare_list_columns : list[ComparisonItem.Columns] | None, optional
                List of column info to compare.

            Returns
            -------
            dict[str, MultipleImputation]
                Dictionary with keys ["difference", "ratio"] containing
                MultipleImputation objects with comparison results and proper
                MI standard errors for the comparisons.

            Examples
            --------
            Compare mi_news to sc_survey (StatCalculator)
            >>> comparison = mi_news.compare(
            ...     sc_survey
            ... )

            Compare means vs medians:
            >>> comparison = mi_means.compare(
            ...     mi_medians,
            ...     compare_list_columns=compare_list_variables=[
            ...     ComparisonItem.Variable(
            ...         "mean",
            ...         "median",
            ...         name="median_mean"
            ...     )]
            ... )
            >>> comparison["difference"].print()

            Compare specific variables:

            >>> comparison = mi_results1.compare(
            ...     mi_results2,
            ...     compare_list_variables=[ComparisonItem.Variable(
            ...         value1="income",
            ...         value2="income_2",
            ...         name="income_comp"
            ...     )]
            ... )
            """

            return kit_comparisons.compare(
                stats1=self,
                stats2=other,
                join_on=self.join_on,
                rounding=self.rounding,
                difference=difference,
                ratio=ratio,
                ratio_minus_1=ratio_minus_1,
                replicate_name=replicate_name,
                compare_list_variables=compare_list_variables,
                compare_list_columns=compare_list_columns,
            )

        def round_results(
            self,
            df: IntoFrameT = None,
            rounding: Rounding | None = None,
            display_only: bool = False,
        ) -> IntoFrameT:
            """
            Apply rounding rules to MI estimates.

            Parameters
            ----------
            df : IntoFrameT, optional
                Table of estimates to round. Default is df_estimates.
            rounding : Rounding|None, optional
                Rounding configuration (True for DRB rules, int for significant digits).
                Default is self.rounding.
            display_only : bool, optional
                If True, converts numbers to strings for display only. Default is False.

            Returns
            -------
            IntoFrameT
                The dataframe with rounding applied.
            """

            if df is None:
                df = self.df_estimates

            if rounding is None:
                rounding = self.rounding

            if df is not None:
                df = drb_round_table(
                    df=df,
                    columns=rounding.cols_round,
                    columns_n=rounding.cols_n,
                    columns_exclude=rounding.cols_exclude,
                    round_all=rounding.round_all,
                    digits=rounding.round_digits,
                    display_only=display_only,
                )

            return df

        def print(self, round_output: bool | int | None = None, sub_log: logging = None):
            """
            Print the MI estimates and standard errors to the log.

            Parameters
            ----------
            round_output : bool|int|None, optional
                Rounding rule (True for DRB, int for significant digits).
                Default is self.rounding configuration.
            sub_log : logging, optional
                Alternative logger to use. Default is None (use standard logging).

            Examples
            --------
            >>> mi_results.print(round_output=True)  # Use DRB rounding
            >>> mi_results.print(round_output=3)     # 3 significant digits
            """

            if sub_log is None:
                sub_log = logger

            #   Round?
            if round_output:
                if self.rounding is None:
                    rounding = Rounding()
                else:
                    rounding = deepcopy(self.rounding)
                rounding.set_round_digits(round_output)

                df_estimates = self.round_results(
                    df=self.df_estimates, rounding=rounding, display_only=True
                )
                df_ses = self.round_results(
                    df=self.df_ses, rounding=rounding, display_only=True
                )
            else:
                df_estimates = self.df_estimates
                df_ses = self.df_ses

            print_se_table(
                df_estimates=df_estimates,
                df_ses=df_ses,
                # display_all_vars=self.display_all_vars,
                # display_max_vars=self.display_max_vars,
                sort_vars=self.join_on,
                round_output=False,
                sub_log=sub_log,
            )

        def table_of_estimates(
            self,
            round_output: bool | int | None = None,
            estimates_to_show: list[str] | None = None,
            variable_prefix: str = "",
            estimate_type_variable_name: str = "Statistic",
            ci_level: float = 0.95,
        ) -> IntoFrameT:
            """
            Create a formatted table combining different types of estimates.

            Reshapes estimates into a long format table with different statistic
            types (estimates, SEs, t-stats, p-values, etc.) as separate rows.

            Parameters
            ----------
            round_output : bool|int|None, optional
                Rounding rule for display.
            estimates_to_show : list[str] | None, optional
                List of estimate types to include. Options:
                - "estimate": Point estimates
                - "se": Standard errors
                - "t": T-statistics
                - "p": P-values
                - "ci": Confidence intervals
                - "df": Degrees of freedom
                Default is ["estimate", "se"].
            variable_prefix : str, optional
                Prefix to add to variable column names. Default is "".
            estimate_type_variable_name : str, optional
                Name for column indicating statistic type. Default is "Statistic".
            ci_level : float, optional
                Confidence level for confidence intervals. Default is 0.95.

            Returns
            -------
            IntoFrameT
                Formatted table with estimates arranged by statistic type.

            Examples
            --------
            >>> table = mi_results.table_of_estimates(
            ...     estimates_to_show=["estimate", "se", "p", "ci"],
            ...     round_output=True
            ... )
            """
            if estimates_to_show is None:
                estimates_to_show = ["estimate", "se"]

            df_ordered = []
            col_sort = "__order_output_table__"
            for index, esti in enumerate(estimates_to_show):
                if esti.lower() == "estimate":
                    df_ordered.append(
                        nw.from_native(self.df_estimates)
                        .with_columns(
                            [
                                nw.lit(index).alias(col_sort),
                                nw.lit(esti.lower()).alias(estimate_type_variable_name),
                            ]
                        )
                        .to_native()
                    )
                elif esti.lower() == "se":
                    df_ordered.append(
                        nw.from_native(self.df_ses)
                        .with_columns(
                            [
                                nw.lit(index).alias(col_sort),
                                nw.lit(esti.lower()).alias(estimate_type_variable_name),
                            ]
                        )
                        .to_native()
                    )
                elif esti.lower() == "t":
                    df_ordered.append(
                        nw.from_native(self.df_t)
                        .with_columns(
                            [
                                nw.lit(index).alias(col_sort),
                                nw.lit(esti.lower()).alias(estimate_type_variable_name),
                            ]
                        )
                        .to_native()
                    )
                elif esti.lower() == "p":
                    cols_to_keep = safe_columns(
                        nw.from_native(self.df_estimates)
                        .lazy()
                        .with_columns(
                            [
                                nw.lit(index).alias(col_sort),
                                nw.lit(esti.lower()).alias(estimate_type_variable_name),
                            ]
                        )
                        .to_native()
                    )

                    df_p = (
                        nw.from_native(self.df_p)
                        .with_columns(
                            [
                                nw.lit(index).alias(col_sort),
                                nw.lit(esti.lower()).alias(estimate_type_variable_name),
                            ]
                        )
                        .select(cols_to_keep)
                        .to_native()
                    )

                    when_then_censor_absurd_values = []
                    absurd_value_threshold = 1e-10
                    #   I don't want to see p-values below a ridiculously low number
                    for coli in self.df_estimates.columns:
                        if coli not in self.join_on:
                            ci = nw.col(coli)
                            when_then_censor_absurd_values.append(
                                (
                                    (
                                        nw.when(ci.lt(absurd_value_threshold))
                                        .then(nw.lit(0.0))
                                        .otherwise(ci)
                                    ).alias(coli)
                                )
                            )

                    df_ordered.append(
                        nw.from_native(df_p)
                        .with_columns(when_then_censor_absurd_values)
                        .to_native()
                    )

                elif esti.lower() == "ci":
                    df_ordered.append(
                        nw.from_native(self._df_ci(ci_level=ci_level))
                        .with_columns(
                            [
                                nw.lit(index).alias(col_sort),
                                nw.lit(esti.lower()).alias(estimate_type_variable_name),
                            ]
                        )
                        .to_native()
                    )
                elif esti.lower() == "df":
                    with_infinites = []
                    for coli in self.summarize_vars:
                        c_coli = nw.col(coli)

                        upper_limit = 10**7
                        with_infinites.append(
                            (
                                nw.when(c_coli.gt(upper_limit))
                                .then(nw.lit(upper_limit))
                                .otherwise(c_coli)
                                .alias(coli)
                            )
                        )

                    df_ordered.append(
                        nw.from_native(self.df_df)
                        .with_columns(with_infinites)
                        .with_columns(
                            [
                                nw.lit(index).alias(col_sort),
                                nw.lit(esti.lower()).alias(estimate_type_variable_name),
                            ]
                        )
                    )
                else:
                    message = f"{esti} not allowed for estimates_to_show"
                    logger.error(message)
                    raise Exception(message)

            col_row_index = "___estimate_row_count___"
            df_ordered[0] = (
                nw.from_native(df_ordered[0]).with_row_index(col_row_index).to_native()
            )

            df_display = concat_wrapper(df_ordered, how="diagonal")

            nw_type = NarwhalsType(df_display)
            df_display = nw_type.to_polars()

            sort_vars = self.join_on
            df_display = df_display.sort(sort_vars + [col_sort]).with_columns(
                pl.col(col_row_index).forward_fill()
            )
            df_display = df_display.sort([col_row_index] + [col_sort]).drop(col_row_index)

            #   Clear extraneous information
            with_clear = []
            for coli in sort_vars:
                c_col = pl.col(coli)
                with_clear.append(
                    pl.when(pl.col(col_sort) != 0)
                    .then(pl.lit(""))
                    .otherwise(c_col.cast(pl.String))
                    .alias(coli)
                )

            select_order = sort_vars + [estimate_type_variable_name]
            remaining = []
            rename = {}
            for coli in df_display.columns:
                if coli not in select_order and coli != col_sort:
                    if variable_prefix != "":
                        rename[coli] = f"{variable_prefix}{coli}"

                    remaining.append(coli)

            df_display = df_display.with_columns(with_clear).select(
                select_order + remaining
            )
            #   Round?
            if round_output:
                if self.rounding is not None:
                    rounding = deepcopy(self.rounding)
                else:
                    rounding = Rounding()
                rounding.set_round_digits(round_output)

                if (
                    len(rounding.cols_n) == 0
                    and len(rounding.cols_round) == 0
                    and not rounding.round_all
                ):
                    #   Nothing set to round, round all
                    rounding.cols_round = remaining

                df_display = self.round_results(
                    df=df_display, rounding=rounding, display_only=True
                )

            if len(rename):
                df_display = df_display.rename(rename)
            return nw_type.from_polars(df_display)

        def _df_ci(self, ci_level: float = 0.95):
            #   Use scipy to get the t-stat ci multiple
            def to_ci_multiple(value) -> float:
                return scipy_stats.t.ppf(1 - (1 - ci_level) / 2, value)

            nw_type = NarwhalsType(self.df_df)
            dof = (
                nw_type.to_polars.lazy()
                .collect()
                .with_columns(
                    pl_cs.numeric().map_elements(to_ci_multiple, return_dtype=pl.Float64)
                )
            )

            #   Use numpy to multiply the se by the t-stat ci multiple
            se_np = (
                nw.from_native(self.df_ses).select(cs.numeric()).lazy().collect().to_numpy()
            )
            dof_np = nw.from_native(dof).select(cs.numeric()).lazy().collect().to_numpy()

            #   return the data
            dof = pl.concat(
                [
                    dof.select(self.join_on),
                    pl.from_numpy(
                        se_np * dof_np,
                        schema={
                            coli: pl.Float64
                            for coli in safe_columns(dof.select(cs.numeric()))
                        },
                    ),
                ],
                how="horizontal",
            )

            return nw_type.from_polars(dof)

        def filter(self, filter_expr: nw.Expr) -> MultipleImputation:
            #   Don't edit the underlying object
            self = self.copy()

            for dfi_name in self._df_attributes:
                apply_as_attribute(
                    obj=self, df_name=dfi_name, nw_expr=filter_expr, nw_method="filter"
                )

            for repi in range(0, len(self.implicate_stats)):
                self.implicate_stats[repi].filter(filter_expr)

            return self

        def select(
            self, select_expr: nw.Expr | str | list[str] | list[nw.Expr]
        ) -> MultipleImputation:
            self = self.copy()
            select_expr = list_input(select_expr)
            cols_keep = columns_from_list(self.df_estimates, columns=select_expr)

            select_df_p = []
            for coli in cols_keep:
                cols_check = [f"{coli}_df", f"{coli}_t"]

                for checki in cols_check:
                    if checki in safe_columns(self.df_p):
                        select_df_p.append(checki)

            add_join_on = list(set(self.join_on).difference(cols_keep))
            cols_keep = add_join_on + cols_keep

            for dfi in self._df_attributes:
                if dfi == "df_p":
                    apply_as_attribute(
                        obj=self,
                        df_name=dfi,
                        nw_expr=cols_keep + select_df_p,
                        nw_method="select",
                    )
                else:
                    apply_as_attribute(
                        obj=self, df_name=dfi, nw_expr=cols_keep, nw_method="select"
                    )

                for repi in range(0, len(self.implicate_stats)):
                    self.implicate_stats[repi].select(cols_keep)
            return self

        def with_columns(self, with_expr: nw.Expr | list[nw.Expr]) -> MultipleImputation:
            self = self.copy()

            for dfi in self._df_attributes:
                apply_as_attribute(
                    obj=self, df_name=dfi, nw_expr=with_expr, nw_method="with_columns"
                )

            for repi in range(0, len(self.implicate_stats)):
                self.implicate_stats[repi].with_columns(with_expr)
            return self

        def rename(self, d_rename: dict[str, str]) -> MultipleImputation:
            self = self.copy()

            for dfi in self._df_attributes:
                apply_as_attribute(
                    obj=self, df_name=dfi, nw_expr=d_rename, nw_method="rename"
                )

            for repi in range(0, len(self.implicate_stats)):
                self.implicate_stats[repi].rename(d_rename)

            return self

        def scale_by(
            self, factor: float, columns: list[str] | str | None = None
        ) -> MultipleImputation:
            if columns is None:
                #   Any columns that aren't the join_on ones
                columns = list(
                    set(safe_columns(self.df_estimates)).difference(self.join_on)
                )

            return self.with_columns(with_expr=nw.col(columns) * factor)

        def pipe(self, function: Callable, *args, **kwargs) -> MultipleImputation:
            """
            Pipe a function to df_estimates, df_ses, and df_replicates (as necessary)

            Parameters
            ----------
            function : Callable
                Function to pipe.
            *args : TYPE
                arguments to function
            **kwargs : TYPE
                keyword arguments to function

            Returns
            -------
            None.

            """

            self = self.copy()

            for dfi_name in self._df_attributes:
                dfi = getattr(self, dfi_name)
                if dfi is not None:
                    setattr(
                        self,
                        dfi_name,
                        nw.to_native(function(nw.from_native(dfi), *args, **kwargs)),
                    )

            for repi in range(0, len(self.implicate_stats)):
                self.implicate_stats[repi].pipe(function, *args, **kwargs)

            return self

        def concat_with(
            self, mi_concat: MultipleImputation, how: str = "horizontal"
        ) -> MultipleImputation:
            """
            Concatenate this with another mi object

            Parameters
            ----------
            mi_concat : MultipleImputation
                Other mi object to concatenate with.
            how : str, optional
                horizontal or vertical?
                Horizontal will actually do a join and vertical will just stack them
                The default is "horizontal".

            Returns
            -------
            MultipleImputation

            """

            self = self.copy()

            def _concat_df(df: IntoFrameT, df_join: IntoFrameT) -> IntoFrameT:
                if how == "horizontal":
                    return join_wrapper(
                        df=df,
                        df_to=df_join,
                        how="left",
                        left_on=self.join_on,
                        right_on=mi_concat.join_on,
                    )
                elif how == "vertical":
                    return concat_wrapper([df, df_join], how="horizontal")

            for dfi in self._df_attributes:
                setattr(
                    self,
                    dfi,
                    _concat_df(df=getattr(self, dfi), df_join=getattr(mi_concat, dfi)),
                )

            for repi in range(0, len(self.implicate_stats)):
                self.implicate_stats[repi].concat_with(
                    rs_concat=mi_concat.implicate_stats[repi],
                    join_on_self=self.join_on,
                    join_on_concat=mi_concat.join_on,
                )

            return self

        def sort(
            self, sort_expr: nw.Expr | list[nw.Expr] | str | list[str]
        ) -> MultipleImputation:
            self = self.copy()
            for dfi in self._df_attributes:
                apply_as_attribute(
                    obj=self, df_name=dfi, nw_expr=sort_expr, nw_method="sort"
                )

            for repi in range(0, len(self.implicate_stats)):
                self.implicate_stats[repi].sort(sort_expr)

            return self

        def drop(
            self, drop_expr: nw.Expr | list[nw.Expr] | str | list[str]
        ) -> MultipleImputation:
            self = self.copy()
            for dfi in self._df_attributes:
                apply_as_attribute(
                    obj=self, df_name=dfi, nw_expr=drop_expr, nw_method="drop"
                )

            for repi in range(0, len(self.implicate_stats)):
                self.implicate_stats[repi].drop(drop_expr)

            return self

        # def reshape_groups_wide_long(self,
        #                              copy:bool=False,
        #                              group_first:bool=True,
        #                              group_col:str="Group",
        #                              invert_group:bool=False) -> MultipleImputation:
        #     if copy:
        #         self = self.copy()

        #     def _reshape(df:IntoFrameT,
        #                  join_on:list[str]) -> IntoFrameT:
        #         if "___replicate___" in df.columns:
        #             join_on = join_on + ["___replicate___"]

        #         df_concat_by_groups = {}
        #         for coli in df.columns:
        #             if coli not in join_on:
        #                 coli_group = coli.split(":")[0]
        #                 coli_value = coli.split(":")[1]
        #                 c_name = pl.col(join_on[0])
        #                 rename = {coli:coli_value}

        #                 if group_first:
        #                     with_name = pl.concat_str([pl.lit(coli_group),
        #                                                pl.lit(":"),
        #                                                c_name]).alias(c_name.meta.output_name())
        #                 else:
        #                     with_name = pl.concat_str([c_name,
        #                                                pl.lit(":"),
        #                                                pl.lit(coli_group)]).alias(c_name.meta.output_name())

        #                 with_name = with_name.alias(c_name.meta.output_name())

        #                 if group_col != "":
        #                     if invert_group:
        #                         with_name = [with_name,
        #                                      c_name.alias(group_col)]
        #                     else:
        #                         with_name = [with_name,
        #                                      pl.lit(coli_group).alias(group_col)]

        #                 dfi = (df.select(join_on + [coli])
        #                          .rename(rename)
        #                          .with_columns(with_name))
        #                 if coli_group in df_concat_by_groups.keys():
        #                     df_concat_by_groups[coli_group].append(dfi)
        #                 else:
        #                     df_concat_by_groups[coli_group] = [dfi]
        #                 # df_concat.append((df.select(join_on + [coli])
        #                 #                     .rename(rename)
        #                 #                     .with_columns(with_name)))

        #         df_concat = []
        #         for keyi, itemi in df_concat_by_groups.items():
        #             if len(itemi) == 1:
        #                 df_concat.append(itemi)
        #             else:
        #                 if group_col != "":
        #                     join_on_group = join_on + [group_col]
        #                 else:
        #                     join_on_group = join_on

        #                 df_concat.append(JoinFileList_Simple(itemi,
        #                                                      Join="outer",
        #                                                      JoinOn=join_on_group))

        #         df_concat = pl.concat(df_concat,
        #                               how="diagonal_relaxed")

        #         return df_concat

        #     self = self.pipe(_reshape,
        #                      join_on=self.join_on)

        #     return self

        def drb_round_table(
            self,
            columns: list | str | None = None,
            columns_n: list | str | None = None,
            columns_exclude: list | str | None = None,
            round_all: bool = True,
            digits: int = 4,
            compress: bool = False,
        ) -> MultipleImputation:
            kwargs = copy(locals())
            del kwargs["self"]
            self.pipe(function=drb_round_table, **kwargs)

            return self

        @property
        def _df_attributes(self) -> list[str]:
            return [
                "df_estimates",
                "df_ses",
                "df_df",
                "df_t",
                "df_p",
                "df_rate_of_missing_information",
            ]

        @property
        def n_implicates(self) -> int:
            return len(self.implicate_stats)

        @property
        def summarize_vars(self) -> list:
            return self.implicate_stats[0].df_estimates.drop(self.join_on).columns

        @classmethod
        def concat(cls, mi_list: list[MultipleImputation]) -> MultipleImputation:
            from .comparisons import _append_to_mi

            mi_out = mi_list[0]

            for i in range(1, len(mi_list)):
                mi_out = _append_to_mi(
                    name="",
                    stat_item=mi_out,
                    stats=mi_list[i],
                    vertical=True,
                    n_implicates=mi_out.n_implicates,
                    vertical_drop_var_name=False,
                    separator="",
                )

            return mi_out

### calculate

    calculate(implicate_name='___implicate___')

Calculate multiple imputation estimates using Rubin's rules.

Combines estimates from individual implicates to produce final MI estimates, standard errors, degrees of freedom, t-statistics, p-values, and rates of missing information. Implements the standard MI combining formulas.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`implicate_name` | `str` | Column name identifier for imputation number. Default is "implicate". | `'___implicate___'`

Notes

Implements Rubin's combining rules: - Q̄ = (1/m) Σ Q̂ᵢ (combined estimate) - U = (1/m) Σ Uᵢ (within-imputation variance) - B = (1/(m-1)) Σ (Q̂ᵢ - Q̄)² (between-imputation variance) - T = U + (1 + 1/m)B (total variance) - ν = (m-1)[1 + mU/((m+1)B)]² (degrees of freedom)

where m is the number of implicates.

Source code in `src\survey_kit\statistics\multiple_imputation.py`

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    def calculate(self, implicate_name="___implicate___"):
        """
        Calculate multiple imputation estimates using Rubin's rules.

        Combines estimates from individual implicates to produce final MI estimates,
        standard errors, degrees of freedom, t-statistics, p-values, and rates of
        missing information. Implements the standard MI combining formulas.

        Parameters
        ----------
        implicate_name : str, optional
            Column name identifier for imputation number. Default is "___implicate___".

        Notes
        -----
        Implements Rubin's combining rules:
        - Q̄ = (1/m) Σ Q̂ᵢ  (combined estimate)
        - U = (1/m) Σ Uᵢ    (within-imputation variance)
        - B = (1/(m-1)) Σ (Q̂ᵢ - Q̄)²  (between-imputation variance)
        - T = U + (1 + 1/m)B  (total variance)
        - ν = (m-1)[1 + mU/((m+1)B)]²  (degrees of freedom)

        where m is the number of implicates.
        """

        df_estimates_stacked = []
        df_ses_stacked = []

        col_sort = "___mi_sort___"
        for indexi, imp_statsi in enumerate(self.implicate_stats):
            if indexi == 0:
                df_sort = (
                    nw.from_native(imp_statsi.df_estimates)
                    .select(self.join_on)
                    .lazy()
                    .collect()
                    .with_row_index(col_sort)
                    .lazy()
                    .to_native()
                )
            df_estimates_stacked.append(imp_statsi.df_estimates)
            df_ses_stacked.append(imp_statsi.df_ses)

        df_estimates_stacked = (
            nw.from_native(
                fill_missing(
                    concat_wrapper(df_estimates_stacked, how="diagonal"),
                    value=float("nan"),
                )
            )
            .lazy()
            .collect()
            .to_native()
        )
        df_ses_stacked = (
            nw.from_native(concat_wrapper(df_ses_stacked, how="diagonal"))
            .with_columns(cs.boolean().cast(nw.Int8))
            .lazy()
            .collect()
            .to_native()
        )

        cols_non_stats = self.join_on + [implicate_name, col_sort]
        cols_stats = safe_columns(df_estimates_stacked)
        cols_stats = _columns_original_order(
            columns_unordered=list(set(cols_stats).difference(cols_non_stats)),
            columns_ordered=cols_stats,
        )

        #   Notation from Joe Schaffer MI FAQ page (downloaded from the Wayback Machine)
        #       NEWS/Documentation/Background/MultipleImputation/MI_FAQ.htm
        df_estimates = (
            nw.from_native(df_estimates_stacked)
            .group_by(self.join_on)
            .agg(nw.all().mean())
            .sort(self.join_on)
        )

        c_stats = nw.col(cols_stats)
        with_between = []
        for coli in cols_stats:
            c_col = nw.col(coli)
            c_bar = nw.col(f"{coli}_bar")
            with_between.append(
                (1 / (self.n_implicates - 1) * (c_col - c_bar) ** 2).alias(coli)
            )

        df_B = (
            nw.from_native(
                join_list(
                    [
                        df_estimates_stacked,
                        (
                            nw.from_native(df_estimates)
                            .rename({coli: f"{coli}_bar" for coli in cols_stats})
                            .to_native()
                        ),
                    ],
                    on=self.join_on,
                    how="left",
                )
            )
            .with_columns(with_between)
            .group_by(self.join_on)
            .agg(c_stats.sum())
            .to_native()
        )

        df_U = (
            nw.from_native(df_ses_stacked)
            .with_columns(c_stats**2)
            .group_by(self.join_on)
            .agg(nw.all().mean())
            .to_native()
        )

        df_variance = (
            nw.from_native(
                concat_wrapper(
                    [
                        nw.from_native(df_B)
                        .with_columns(c_stats * (1 + 1 / self.n_implicates))
                        .to_native(),
                        df_U,
                    ],
                    how="diagonal",
                )
            )
            .group_by(self.join_on)
            .agg(nw.all().sum())
            .to_native()
        )

        self.df_ses = nw.from_native(df_variance).with_columns(c_stats**0.5).to_native()

        self.df_estimates = (
            nw.from_native(df_estimates_stacked)
            .group_by(self.join_on)
            .agg(nw.all().mean())
            .sort(self.join_on)
            .to_native()
        )

        df_B_U = join_list(
            [
                (
                    nw.from_native(df_B)
                    .rename({coli: f"{coli}_B" for coli in cols_stats})
                    .to_native()
                ),
                (
                    nw.from_native(df_U)
                    .rename({coli: f"{coli}_U" for coli in cols_stats})
                    .to_native()
                ),
            ],
            on=self.join_on,
            how="left",
        )

        m = self.n_implicates
        with_df = []
        for coli in cols_stats:
            c_U = nw.col(f"{coli}_U")
            c_B = nw.col(f"{coli}_B")

            with_df.append(
                ((m - 1) * (1 + (m * c_U) / ((m + 1) * c_B)) ** 2).alias(coli)
            )

        self.df_df = nw.from_native(df_B_U).select(self.join_on + with_df).to_native()

        with_r = []
        with_gamma = []
        for coli in cols_stats:
            c_U = nw.col(f"{coli}_U")
            c_B = nw.col(f"{coli}_B")
            c_r = nw.col(f"{coli}_r")
            c_df = nw.col(f"{coli}_df")
            with_r.append(((1 + 1 / m) * c_B / c_U).alias(f"{coli}_r"))

            with_gamma.append(((c_r + (2 / (c_df + 3))) / (c_r + 1)).alias(coli))

        self.df_rate_of_missing_information = (
            nw.from_native(
                join_list(
                    [
                        df_B_U,
                        (
                            nw.from_native(self.df_df)
                            .rename({coli: f"{coli}_df" for coli in cols_stats})
                            .to_native()
                        ),
                    ],
                    how="left",
                    on=self.join_on,
                )
            )
            .with_columns(with_r)
            .select(self.join_on + with_gamma)
            .to_native()
        )

        with_t = []
        for coli in cols_stats:
            c_est = nw.col(coli)
            c_se = nw.col(f"{coli}_se")

            with_t.append((c_est / c_se).abs().alias(coli))

        self.df_t = (
            nw.from_native(
                join_list(
                    [
                        self.df_estimates,
                        (
                            nw.from_native(self.df_ses)
                            .rename({coli: f"{coli}_se" for coli in cols_stats})
                            .to_native()
                        ),
                    ],
                    on=self.join_on,
                    how="left",
                )
            )
            .select(self.join_on + with_t)
            .to_native()
        )

        df_p = join_list(
            [
                (
                    nw.from_native(self.df_df)
                    .rename({coli: f"{coli}_df" for coli in cols_stats})
                    .to_native()
                ),
                (
                    nw.from_native(self.df_t)
                    .rename({coli: f"{coli}_t" for coli in cols_stats})
                    .to_native()
                ),
            ],
            how="left",
            on=self.join_on,
        )

        def p_value(t, df):
            if t == float("inf") or t == float("nan"):
                return 0
            if df == float("inf") or df == float("nan"):
                df = 1_000_000

            return scipy.stats.t.sf(t, df) * 2

        def p_value_lambda(t, col_t, col_df):
            try:
                return p_value(t[col_t], t[col_df])
            except:
                return None

        nw_type = NarwhalsType(df_p)
        df_p = nw_type.to_polars().lazy().collect()
        for coli in cols_stats:
            index_t = df_p.columns.index(f"{coli}_t")
            index_df = df_p.columns.index(f"{coli}_df")

            df_p = df_p.with_columns(
                df_p.map_rows(
                    lambda t: p_value_lambda(t, index_t, index_df),
                    return_dtype=pl.Float64,
                )
            ).rename({"map": coli})

        self.df_p = nw_type.from_polars(df_p.select(self.join_on + cols_stats))

        def _sort_and_fill_null(df: IntoFrameT) -> IntoFrameT:
            nw_type = NarwhalsType(
                join_list([df, df_sort], how="left", on=self.join_on)
            )
            return nw_type.from_polars(
                nw_type.to_polars()
                .sort([col_sort], maintain_order=True)
                .drop(col_sort)
                .fill_nan(None)
            )

        self.df_estimates = _sort_and_fill_null(self.df_estimates)
        self.df_ses = _sort_and_fill_null(self.df_ses)
        self.df_df = _sort_and_fill_null(self.df_df)
        self.df_t = _sort_and_fill_null(self.df_t)
        self.df_p = _sort_and_fill_null(df_p)
        self.df_rate_of_missing_information = _sort_and_fill_null(
            self.df_rate_of_missing_information
        )

### compare

    compare(
        other: ReplicateStats
        | MultipleImputation
        | StatCalculator,
        difference: bool = True,
        ratio: bool = True,
        ratio_minus_1: bool = True,
        replicate_name: str = "___replicate___",
        compare_list_variables: list[Variable] | None = None,
        compare_list_columns: list[Column] | None = None,
    ) -> dict[str, MultipleImputation]

Compare this set of MI estimates to another set of estimates.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`other` | `MultipleImputation | ReplicateStats | StatCalculator` | The other object to compare against. | required
`difference` | `bool` | Calculate and return differences. Default is True. | `True`
`ratio` | `bool` | Calculate and return ratios. Default is True. | `True`
`ratio_minus_1` | `bool` | Subtract 1 from ratios (for percentage change interpretation). Default is True. | `True`
`replicate_name` | `str` | Column name for replicate identifier. Default is "replicate". | `'___replicate___'`
`compare_list_variables` | `list[Variable] | None` | List of variable info to compare. | `None`
`compare_list_columns` | `list[Columns] | None` | List of column info to compare. | `None`

Returns:

Type | Description
--- | ---
`dict[str, MultipleImputation]` | Dictionary with keys ["difference", "ratio"] containing MultipleImputation objects with comparison results and proper MI standard errors for the comparisons.

Examples:

Compare mi_news to sc_survey (StatCalculator)

    >>> comparison = mi_news.compare(
    ...     sc_survey
    ... )

Compare means vs medians:

    >>> comparison = mi_means.compare(
    ...     mi_medians,
    ...     compare_list_columns=compare_list_variables=[
    ...     ComparisonItem.Variable(
    ...         "mean",
    ...         "median",
    ...         name="median_mean"
    ...     )]
    ... )
    >>> comparison["difference"].print()

Compare specific variables:

    >>> comparison = mi_results1.compare(
    ...     mi_results2,
    ...     compare_list_variables=[ComparisonItem.Variable(
    ...         value1="income",
    ...         value2="income_2",
    ...         name="income_comp"
    ...     )]
    ... )

Source code in `src\survey_kit\statistics\multiple_imputation.py`

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    def compare(
        self,
        other: ReplicateStats | MultipleImputation | StatCalculator,
        difference: bool = True,
        ratio: bool = True,
        ratio_minus_1: bool = True,
        replicate_name: str = "___replicate___",
        compare_list_variables: list[ComparisonItem.Variable] | None = None,
        compare_list_columns: list[ComparisonItem.Column] | None = None,
    ) -> dict[str, MultipleImputation]:
        """
        Compare this set of MI estimates to another set of estimates.

        Parameters
        ----------
        other : MultipleImputation | ReplicateStats | StatCalculator
            The other object to compare against.
        difference : bool, optional
            Calculate and return differences. Default is True.
        ratio : bool, optional
            Calculate and return ratios. Default is True.
        ratio_minus_1 : bool, optional
            Subtract 1 from ratios (for percentage change interpretation).
            Default is True.
        replicate_name : str, optional
            Column name for replicate identifier. Default is "___replicate___".
        compare_list_variables : list[ComparisonItem.Variable] | None, optional
            List of variable info to compare.
        compare_list_columns : list[ComparisonItem.Columns] | None, optional
            List of column info to compare.

        Returns
        -------
        dict[str, MultipleImputation]
            Dictionary with keys ["difference", "ratio"] containing
            MultipleImputation objects with comparison results and proper
            MI standard errors for the comparisons.

        Examples
        --------
        Compare mi_news to sc_survey (StatCalculator)
        >>> comparison = mi_news.compare(
        ...     sc_survey
        ... )

        Compare means vs medians:
        >>> comparison = mi_means.compare(
        ...     mi_medians,
        ...     compare_list_columns=compare_list_variables=[
        ...     ComparisonItem.Variable(
        ...         "mean",
        ...         "median",
        ...         name="median_mean"
        ...     )]
        ... )
        >>> comparison["difference"].print()

        Compare specific variables:

        >>> comparison = mi_results1.compare(
        ...     mi_results2,
        ...     compare_list_variables=[ComparisonItem.Variable(
        ...         value1="income",
        ...         value2="income_2",
        ...         name="income_comp"
        ...     )]
        ... )
        """

        return kit_comparisons.compare(
            stats1=self,
            stats2=other,
            join_on=self.join_on,
            rounding=self.rounding,
            difference=difference,
            ratio=ratio,
            ratio_minus_1=ratio_minus_1,
            replicate_name=replicate_name,
            compare_list_variables=compare_list_variables,
            compare_list_columns=compare_list_columns,
        )

### concat_with

    concat_with(
        mi_concat: MultipleImputation, how: str = "horizontal"
    ) -> MultipleImputation

Concatenate this with another mi object

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`mi_concat` | `MultipleImputation` | Other mi object to concatenate with. | required
`how` | `str` | horizontal or vertical? Horizontal will actually do a join and vertical will just stack them The default is "horizontal". | `'horizontal'`

Returns:

Type | Description
--- | ---
`MultipleImputation` |

Source code in `src\survey_kit\statistics\multiple_imputation.py`

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    def concat_with(
        self, mi_concat: MultipleImputation, how: str = "horizontal"
    ) -> MultipleImputation:
        """
        Concatenate this with another mi object

        Parameters
        ----------
        mi_concat : MultipleImputation
            Other mi object to concatenate with.
        how : str, optional
            horizontal or vertical?
            Horizontal will actually do a join and vertical will just stack them
            The default is "horizontal".

        Returns
        -------
        MultipleImputation

        """

        self = self.copy()

        def _concat_df(df: IntoFrameT, df_join: IntoFrameT) -> IntoFrameT:
            if how == "horizontal":
                return join_wrapper(
                    df=df,
                    df_to=df_join,
                    how="left",
                    left_on=self.join_on,
                    right_on=mi_concat.join_on,
                )
            elif how == "vertical":
                return concat_wrapper([df, df_join], how="horizontal")

        for dfi in self._df_attributes:
            setattr(
                self,
                dfi,
                _concat_df(df=getattr(self, dfi), df_join=getattr(mi_concat, dfi)),
            )

        for repi in range(0, len(self.implicate_stats)):
            self.implicate_stats[repi].concat_with(
                rs_concat=mi_concat.implicate_stats[repi],
                join_on_self=self.join_on,
                join_on_concat=mi_concat.join_on,
            )

        return self

### pipe

    pipe(
        function: Callable, *args, **kwargs
    ) -> MultipleImputation

Pipe a function to df_estimates, df_ses, and df_replicates (as necessary)

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`function` | `Callable` | Function to pipe. | required
`*args` | `TYPE` | arguments to function | `()`
`**kwargs` | `TYPE` | keyword arguments to function | `{}`

Returns:

Type | Description
--- | ---
`None.` |

Source code in `src\survey_kit\statistics\multiple_imputation.py`

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    def pipe(self, function: Callable, *args, **kwargs) -> MultipleImputation:
        """
        Pipe a function to df_estimates, df_ses, and df_replicates (as necessary)

        Parameters
        ----------
        function : Callable
            Function to pipe.
        *args : TYPE
            arguments to function
        **kwargs : TYPE
            keyword arguments to function

        Returns
        -------
        None.

        """

        self = self.copy()

        for dfi_name in self._df_attributes:
            dfi = getattr(self, dfi_name)
            if dfi is not None:
                setattr(
                    self,
                    dfi_name,
                    nw.to_native(function(nw.from_native(dfi), *args, **kwargs)),
                )

        for repi in range(0, len(self.implicate_stats)):
            self.implicate_stats[repi].pipe(function, *args, **kwargs)

        return self

### print

    print(
        round_output: bool | int | None = None,
        sub_log: logging = None,
    )

Print the MI estimates and standard errors to the log.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`round_output` | `bool | int | None` | Rounding rule (True for DRB, int for significant digits). Default is self.rounding configuration. | `None`
`sub_log` | `logging` | Alternative logger to use. Default is None (use standard logging). | `None`

Examples:

    >>> mi_results.print(round_output=True)  # Use DRB rounding
    >>> mi_results.print(round_output=3)     # 3 significant digits

Source code in `src\survey_kit\statistics\multiple_imputation.py`

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    def print(self, round_output: bool | int | None = None, sub_log: logging = None):
        """
        Print the MI estimates and standard errors to the log.

        Parameters
        ----------
        round_output : bool|int|None, optional
            Rounding rule (True for DRB, int for significant digits).
            Default is self.rounding configuration.
        sub_log : logging, optional
            Alternative logger to use. Default is None (use standard logging).

        Examples
        --------
        >>> mi_results.print(round_output=True)  # Use DRB rounding
        >>> mi_results.print(round_output=3)     # 3 significant digits
        """

        if sub_log is None:
            sub_log = logger

        #   Round?
        if round_output:
            if self.rounding is None:
                rounding = Rounding()
            else:
                rounding = deepcopy(self.rounding)
            rounding.set_round_digits(round_output)

            df_estimates = self.round_results(
                df=self.df_estimates, rounding=rounding, display_only=True
            )
            df_ses = self.round_results(
                df=self.df_ses, rounding=rounding, display_only=True
            )
        else:
            df_estimates = self.df_estimates
            df_ses = self.df_ses

        print_se_table(
            df_estimates=df_estimates,
            df_ses=df_ses,
            # display_all_vars=self.display_all_vars,
            # display_max_vars=self.display_max_vars,
            sort_vars=self.join_on,
            round_output=False,
            sub_log=sub_log,
        )

### round_results

    round_results(
        df: IntoFrameT = None,
        rounding: Rounding | None = None,
        display_only: bool = False,
    ) -> IntoFrameT

Apply rounding rules to MI estimates.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`df` | `IntoFrameT` | Table of estimates to round. Default is df_estimates. | `None`
`rounding` | `Rounding | None` | Rounding configuration (True for DRB rules, int for significant digits). Default is self.rounding. | `None`
`display_only` | `bool` | If True, converts numbers to strings for display only. Default is False. | `False`

Returns:

Type | Description
--- | ---
`IntoFrameT` | The dataframe with rounding applied.

Source code in `src\survey_kit\statistics\multiple_imputation.py`

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    def round_results(
        self,
        df: IntoFrameT = None,
        rounding: Rounding | None = None,
        display_only: bool = False,
    ) -> IntoFrameT:
        """
        Apply rounding rules to MI estimates.

        Parameters
        ----------
        df : IntoFrameT, optional
            Table of estimates to round. Default is df_estimates.
        rounding : Rounding|None, optional
            Rounding configuration (True for DRB rules, int for significant digits).
            Default is self.rounding.
        display_only : bool, optional
            If True, converts numbers to strings for display only. Default is False.

        Returns
        -------
        IntoFrameT
            The dataframe with rounding applied.
        """

        if df is None:
            df = self.df_estimates

        if rounding is None:
            rounding = self.rounding

        if df is not None:
            df = drb_round_table(
                df=df,
                columns=rounding.cols_round,
                columns_n=rounding.cols_n,
                columns_exclude=rounding.cols_exclude,
                round_all=rounding.round_all,
                digits=rounding.round_digits,
                display_only=display_only,
            )

        return df

### table_of_estimates

    table_of_estimates(
        round_output: bool | int | None = None,
        estimates_to_show: list[str] | None = None,
        variable_prefix: str = "",
        estimate_type_variable_name: str = "Statistic",
        ci_level: float = 0.95,
    ) -> IntoFrameT

Create a formatted table combining different types of estimates.

Reshapes estimates into a long format table with different statistic types (estimates, SEs, t-stats, p-values, etc.) as separate rows.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`round_output` | `bool | int | None` | Rounding rule for display. | `None`
`estimates_to_show` | `list[str] | None` | List of estimate types to include. Options: - "estimate": Point estimates - "se": Standard errors - "t": T-statistics - "p": P-values - "ci": Confidence intervals - "df": Degrees of freedom Default is ["estimate", "se"]. | `None`
`variable_prefix` | `str` | Prefix to add to variable column names. Default is "". | `''`
`estimate_type_variable_name` | `str` | Name for column indicating statistic type. Default is "Statistic". | `'Statistic'`
`ci_level` | `float` | Confidence level for confidence intervals. Default is 0.95. | `0.95`

Returns:

Type | Description
--- | ---
`IntoFrameT` | Formatted table with estimates arranged by statistic type.

Examples:

    >>> table = mi_results.table_of_estimates(
    ...     estimates_to_show=["estimate", "se", "p", "ci"],
    ...     round_output=True
    ... )

Source code in `src\survey_kit\statistics\multiple_imputation.py`

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    def table_of_estimates(
        self,
        round_output: bool | int | None = None,
        estimates_to_show: list[str] | None = None,
        variable_prefix: str = "",
        estimate_type_variable_name: str = "Statistic",
        ci_level: float = 0.95,
    ) -> IntoFrameT:
        """
        Create a formatted table combining different types of estimates.

        Reshapes estimates into a long format table with different statistic
        types (estimates, SEs, t-stats, p-values, etc.) as separate rows.

        Parameters
        ----------
        round_output : bool|int|None, optional
            Rounding rule for display.
        estimates_to_show : list[str] | None, optional
            List of estimate types to include. Options:
            - "estimate": Point estimates
            - "se": Standard errors
            - "t": T-statistics
            - "p": P-values
            - "ci": Confidence intervals
            - "df": Degrees of freedom
            Default is ["estimate", "se"].
        variable_prefix : str, optional
            Prefix to add to variable column names. Default is "".
        estimate_type_variable_name : str, optional
            Name for column indicating statistic type. Default is "Statistic".
        ci_level : float, optional
            Confidence level for confidence intervals. Default is 0.95.

        Returns
        -------
        IntoFrameT
            Formatted table with estimates arranged by statistic type.

        Examples
        --------
        >>> table = mi_results.table_of_estimates(
        ...     estimates_to_show=["estimate", "se", "p", "ci"],
        ...     round_output=True
        ... )
        """
        if estimates_to_show is None:
            estimates_to_show = ["estimate", "se"]

        df_ordered = []
        col_sort = "__order_output_table__"
        for index, esti in enumerate(estimates_to_show):
            if esti.lower() == "estimate":
                df_ordered.append(
                    nw.from_native(self.df_estimates)
                    .with_columns(
                        [
                            nw.lit(index).alias(col_sort),
                            nw.lit(esti.lower()).alias(estimate_type_variable_name),
                        ]
                    )
                    .to_native()
                )
            elif esti.lower() == "se":
                df_ordered.append(
                    nw.from_native(self.df_ses)
                    .with_columns(
                        [
                            nw.lit(index).alias(col_sort),
                            nw.lit(esti.lower()).alias(estimate_type_variable_name),
                        ]
                    )
                    .to_native()
                )
            elif esti.lower() == "t":
                df_ordered.append(
                    nw.from_native(self.df_t)
                    .with_columns(
                        [
                            nw.lit(index).alias(col_sort),
                            nw.lit(esti.lower()).alias(estimate_type_variable_name),
                        ]
                    )
                    .to_native()
                )
            elif esti.lower() == "p":
                cols_to_keep = safe_columns(
                    nw.from_native(self.df_estimates)
                    .lazy()
                    .with_columns(
                        [
                            nw.lit(index).alias(col_sort),
                            nw.lit(esti.lower()).alias(estimate_type_variable_name),
                        ]
                    )
                    .to_native()
                )

                df_p = (
                    nw.from_native(self.df_p)
                    .with_columns(
                        [
                            nw.lit(index).alias(col_sort),
                            nw.lit(esti.lower()).alias(estimate_type_variable_name),
                        ]
                    )
                    .select(cols_to_keep)
                    .to_native()
                )

                when_then_censor_absurd_values = []
                absurd_value_threshold = 1e-10
                #   I don't want to see p-values below a ridiculously low number
                for coli in self.df_estimates.columns:
                    if coli not in self.join_on:
                        ci = nw.col(coli)
                        when_then_censor_absurd_values.append(
                            (
                                (
                                    nw.when(ci.lt(absurd_value_threshold))
                                    .then(nw.lit(0.0))
                                    .otherwise(ci)
                                ).alias(coli)
                            )
                        )

                df_ordered.append(
                    nw.from_native(df_p)
                    .with_columns(when_then_censor_absurd_values)
                    .to_native()
                )

            elif esti.lower() == "ci":
                df_ordered.append(
                    nw.from_native(self._df_ci(ci_level=ci_level))
                    .with_columns(
                        [
                            nw.lit(index).alias(col_sort),
                            nw.lit(esti.lower()).alias(estimate_type_variable_name),
                        ]
                    )
                    .to_native()
                )
            elif esti.lower() == "df":
                with_infinites = []
                for coli in self.summarize_vars:
                    c_coli = nw.col(coli)

                    upper_limit = 10**7
                    with_infinites.append(
                        (
                            nw.when(c_coli.gt(upper_limit))
                            .then(nw.lit(upper_limit))
                            .otherwise(c_coli)
                            .alias(coli)
                        )
                    )

                df_ordered.append(
                    nw.from_native(self.df_df)
                    .with_columns(with_infinites)
                    .with_columns(
                        [
                            nw.lit(index).alias(col_sort),
                            nw.lit(esti.lower()).alias(estimate_type_variable_name),
                        ]
                    )
                )
            else:
                message = f"{esti} not allowed for estimates_to_show"
                logger.error(message)
                raise Exception(message)

        col_row_index = "___estimate_row_count___"
        df_ordered[0] = (
            nw.from_native(df_ordered[0]).with_row_index(col_row_index).to_native()
        )

        df_display = concat_wrapper(df_ordered, how="diagonal")

        nw_type = NarwhalsType(df_display)
        df_display = nw_type.to_polars()

        sort_vars = self.join_on
        df_display = df_display.sort(sort_vars + [col_sort]).with_columns(
            pl.col(col_row_index).forward_fill()
        )
        df_display = df_display.sort([col_row_index] + [col_sort]).drop(col_row_index)

        #   Clear extraneous information
        with_clear = []
        for coli in sort_vars:
            c_col = pl.col(coli)
            with_clear.append(
                pl.when(pl.col(col_sort) != 0)
                .then(pl.lit(""))
                .otherwise(c_col.cast(pl.String))
                .alias(coli)
            )

        select_order = sort_vars + [estimate_type_variable_name]
        remaining = []
        rename = {}
        for coli in df_display.columns:
            if coli not in select_order and coli != col_sort:
                if variable_prefix != "":
                    rename[coli] = f"{variable_prefix}{coli}"

                remaining.append(coli)

        df_display = df_display.with_columns(with_clear).select(
            select_order + remaining
        )
        #   Round?
        if round_output:
            if self.rounding is not None:
                rounding = deepcopy(self.rounding)
            else:
                rounding = Rounding()
            rounding.set_round_digits(round_output)

            if (
                len(rounding.cols_n) == 0
                and len(rounding.cols_round) == 0
                and not rounding.round_all
            ):
                #   Nothing set to round, round all
                rounding.cols_round = remaining

            df_display = self.round_results(
                df=df_display, rounding=rounding, display_only=True
            )

        if len(rename):
            df_display = df_display.rename(rename)
        return nw_type.from_polars(df_display)